The hypotenuse of a right-angled triangle is 11m
more than the twice the shortest side. If the third side
is 1 m less than the hypotenuse, find the sides of the
triangle.
Answers
Answer:
10,26,24
Step-by-step explanation:
Let the length of the shortest side be x meters.
Then, hypotenuse=(2x+6) metres
And the third side (2x+6−2) metre=(2x+4) metres
By Pythagoras theorem, we have
(2x+6)
2
=x
2
+(2x+4)
2
⇒x
2
−8x−20=0
⇒x
2
−10x−2x−20=0
⇒(x−10)(x+2)=0
⇒x=10orx=−2
∵ x can not be a negative $$\therefore
⇒x=10
Length of the shortest side =10 metres
Length of the hypotenuse =(2x+6) metres=26 metres
Length of the third side =(2x+4) metres=24 metres
Hence the sides of the triangle are 10m,26m and 24m
Step-by-step explanation:
Let the length of the shortest side be x meters.
Then, hypotenuse=(2x+6) metres
And the third side (2x+6−2) metre=(2x+4) metres
By Pythagoras theorem, we have
(2x+6)
2
=x
2
+(2x+4)
2
⇒x
2
−8x−20=0
⇒x
2
−10x−2x−20=0
⇒(x−10)(x+2)=0
⇒x=10orx=−2
∵ x can not be a negative $$\therefore
⇒x=10
Length of the shortest side =10 metres
Length of the hypotenuse =(2x+6) metres=26 metres
Length of the third side =(2x+4) metres=24 metres
Hence the sides of the triangle are 10 26 and 24